Engineering the band gap and optical properties of a two-dimensional molybdenum carbon fluoride MXene

Using first-principles density functional theory, the electronic and optical properties of monolayer and multilayer nanosheets of molybdenum carbon fluoride (Mo2CF2), a two-dimensional (2D) transition-metal carbide MXene, were investigated. The unique behavior of its optical properties along with the ability to control its electronic and optical properties enhances the potential of 2D Mo2CF2 for various applications in the fields of electronics and energy storage.


Introduction
Since the discovery of graphene and its wonderful properties (Kaushik et al., 2019;Ostovari et al., 2018), two-dimensional (2D) materials with their extraordinary electronic, mechanical and optical properties (Georgiou et al., 2012;Tamleh et al., 2018) have attracted much research interest in the field of materials science. The recent discovery of a novel family of compounds called 2D transition-metal carbides, nitrides and carbonitrides (MXene) has gained significant attention from the scientific community and has spurred new interest in 2D materials (Khazaei et al., 2019;Bae et al., 2021;Naguib et al., 2013;Anasori et al., 2015). MXene has a general formula of M n+1 X n T x (n = 1-3), where M indicates early transition metals (e.g. Sc, Ti, V, Nb, Mo, etc.), X stands for C and/or N, and T x represents functional groups on the surface of the MXene, such as -OH, -O or -F (Naguib et al., 2011;Hong et al., 2020;Champagne et al., 2018). MXenes have a huge potential in a wide range of applications, such as energy storage (Yorulmaz et al., 2016;Anasori et al., 2017), sensing (Sinha et al., 2018;Khazaei et al., 2012), catalysis (Peng et al., 2018;Wang et al., 2018;Li & Wu, 2019) and the development of electronic devices (Zhang & Nicolosi, 2019).
Molybdenum carbon fluoride (Mo 2 CF 2 ) is a MXene consisting of the molybdenum (Mo) transition metal, carbon (C) and functionalized by fluorine (F). Khazaei et al. (2014) reported that a monolayer Mo 2 CF 2 is an indirect band gap semiconductor with a narrow band gap of 0.27 eV and the most stable Mo 2 CF 2 (hollow site-hollow site) structure is a promising thermoelectric material. Monolayer Mo 2 CF 2 has many excellent properties, such as high capacity, outstanding mechanical strength and good flexibility. Therefore, this material has a great potential as an anode material for Li-ion batteries, as well as in various applications, including electronics and energy storage (Mehta et al., 2019).
Despite previous works on several MXenes, including Ti 3 C 2 T 2 , Nb 4 C 3 T x and V 2 C-, with a wide variety of applications (Khazaei et al., 2019;Bae et al., 2021;Champagne et al., 2018;Mostafaei & Abbasnejad, 2021;Khan et al., 2019), research on the electronic and optical properties of Mo 2 CF 2 , and how the number of layers affects these properties is still lacking. The ability to control the band gap of a material is very important for its application in the field of electronic devices. As a material with exciting prospects for electronics and energy storage applications, the ability to control the electronic structure and hence the band gap of Mo 2 CF 2 will greatly enhance its potential. However, the ability to control the band gap of Mo 2 CF 2 has not yet been demonstrated. Therefore, this work investigates the structural, electronic and optical properties of monolayer, bilayer and trilayer nanosheets of Mo 2 CF 2 (collectively referred to as 2D layered Mo 2 CF 2 ) using first-principles calculations in the framework of the generalized gradient approximation (GGA) implemented by the Perdew-Burke-Ernzerhof (PBE) functional. Our results illustrate how the electronic structure, band gap energy and optical properties can be controlled by manipulating the number of layers in a 2D Mo 2 CF 2 .

Computational method
The crystal structures of the bulk and 2D layered Mo 2 CF 2 were visualized using VESTA (Momma & Izumi, 2011). The top and side views of bulk Mo 2 CF 2 are shown in Figs. 1(a) and 1(b). Bulk Mo 2 CF 2 consists of a layer of C atoms sandwiched between Mo atoms and two layers of Mo atoms halogenated by F atomic layers on each side. It has a hexagonal structure and space group P6 3 /mmc (No. 194). The side view of the relaxed configurations of the monolayer, bilayer and trilayer nanosheet is illustrated in Fig. 1. The atomic coordinates used to construct and visualize the bulk structure are Mo1 (0.333, 0.667, 0.368), Mo2 (0.667, 0.333, 0.632), C (0.000, 0.000, 0.500), F1 (0.667, 0.333, 0.184) and F2 (0.333, 0.667, 0.8156). The atomic coordinates (Wyckoff positions) and unit-cell parameters are taken from a previous report (Khazaei et al., 2014) and were optimized using the GGA-PBE functional with the convergence criterion of 510 À6 eV per atom. The Mo-C and Mo-F bonds are strong, with mixed covalent, metallic and ionic characteristics. On the other hand, the F-F bonds are weaker and more reactive, allowing a monolayer to be easily exfoliated from the bulk (Zhu et al., 2017). The structure of the monolayer was constructed in VESTA starting from the 111 unit cell of the bulk crystal and making the value of the c axis five times greater than that of the bulk, thereby obtaining a 115 supercell. The number of layers was increased by adding a layer into the unit cell while keeping the lattice parameter along the c axis fixed. The structure from monolayer to multilayer is optimized every time a layer is added. The optimized unit-cell parameters are shown in Table 1.
The electronic band structures of bulk and 2D layered Mo 2 CF 2 were calculated based on density functional theory (DFT) within the generalized gradient approximation (GGA) using the Perdew-Burke-Ernzerhof (PBE) functional. The calculations were implemented in the CASTEP code (Segall et al., 2002;Accelrys, 2010) with a sufficiently high plane-wave basis cut-off of 500 eV. In all calculations, a 551 Monkhorst-Pack k-point grid was used to generate the initial charge density.
The optical properties of the bulk and 2D layered Mo 2 CF 2 were extracted from the frequency-dependent complex dielectric function after applying a scissors correction to account for the excited-state nature of the optical properties. The complex dielectric function represents the linear response of The crystal structures of Mo 2 CF 2 showing (a) a top view and (b) a side view of bulk Mo 2 CF 2 , and (c) a side view of the monolayer (left), bilayer (middle) and trilayer (right) nanosheets of Mo 2 CF 2 . Table 1 Calculated band gap energy, unit-cell parameters and bond lengths for the bulk and two-dimensional layered Mo 2 CF 2 .
Band gap energy (eV) the system to an external electromagnetic field and consists of a real and imaginary part as follows: where ! is the optical frequency and " 1 (!) and " 2 (!) are the real and imaginary parts of the dielectric function, respectively. The real part " 1 (!) of the dielectric function can be obtained from the imaginary part " 2 (!) using the Kramers-Kronig relationships (Hutchings et al., 1992;Kronig, 1926;Kramers, 1927).
where P is the principal value, is an infinitesimal complex shift with a value of 0.1 and ! is the frequency over which the equation is being integrated. From the frequency-dependent complex dielectric function, other optical parameters, such as the absorption coefficient (!), refractive index n(!), reflectivity R(!) (Qiu et al., 2018) and conductivity () (Accelrys, 2010), were calculated using the following equations, where c is the speed of light: 3. Results and discussion 3.1. Crystal structure and electronic band structure The unit-cell parameters and bond lengths for the bulk and 2D layered Mo 2 CF 2 are summarized in Table 1. Our result for the monolayer is in good agreement with previous reports that numerically calculated the electronic structure of monolayer Mo 2 CF 2 (Khazaei et al., 2014). Experimental results for the band gap energy, unit-cell parameters, and bond lengths of bulk and 2D layered Mo 2 CF 2 are still lacking. Electronic band structures of (a) bulk, (b) monolayer, (c) bilayer and (d) trilayer Mo 2 CF 2 k-points path G-A-H-K-G-M-L-H in the first Brillouin zone. In these figures, the valence band maxima are shifted to zero energy. The band structures exhibit similar band shapes, particularly for the valence and conduction bands. All the materials are seen to be indirect band gap semiconductors. The maximum of the valence band and the minimum of the conduction band of the monolayer and multilayer are located at the k-point between G and K, while the bulk has the band gap located at the k-point between H and A.
The band gap energies of the monolayer, bilayer, trilayer and bulk Mo 2 CF 2 are 0.278, 0.258, 0.249 and 0.237 eV, respectively, as summarized in Table 1. The 0.278 eV band gap energy obtained from our calculations for the monolayer is in good agreement with the previously reported band gap energy of 0.27 eV calculated using GGA-PBE (Khazaei et al., 2014). In general, the band gap energy decreases as the number of layers is increased. The decrease in band gap energy can be attributed to interlayer coupling, which results in the splitting of the bands. As can be seen in Figs. 2(b) (monolayer), 2(c) (bilayer) and 2(d) (trilayer), band splitting increases progressively from the monolayer to the trilayer, and the splitting depends on the number of layers. As the number of layers increases, the splitting of bands due to the stronger interlayer coupling results in a decrease in the band gap energy. In comparison, band splitting in the bulk Mo 2 CF 2 is relatively small, which indicates that the couplings in the bulk are weak van der Waals interactions. These results indicate that the band gap of 2D layered Mo 2 CF 2 could be engineered by controlling the number of layers. The ability to manipulate the band gap energy makes Mo 2 CF 2 a promising material for applications in the field of electronic devices.
The total and partial density of states for the bulk and 2D layered Mo 2 CF 2 are shown in Fig. 3. The valence band maximum and conduction band minimum are mainly composed of Mo-d states with a small overlap with C-p and F-p states. The Mo-d states also play a dominant role in the conduction band above the Fermi level, which confirms the partially occupied Mo 2+ 4d 2 orbital. greater ability for the polarization of low incident photon energy as the number of layers increases. Moving towards higher incident photon energy, an inflection point is observed around 6 eV, where " 1 (!) takes on negative values. Above 6 eV, the intensity of the peaks appears to decrease (becomes more negative) as the number of layers increases. In the photon energy intervals 0.68-2.19, 3.49-6.68 and 7.30-8.31 eV, the bulk and 2D layered Mo 2 CF 2 behave as a metal owing to anomalous dispersion. Dispersion is the property of materials whereby the refractive index changes as a function of wavelength. In normal dispersion, the refractive index increases as the photon energy increases (wavelength decreases), meaning that longer wavelengths are bent less compared to shorter wavelengths. The anomalous dispersion is confirmed by the plot of the refractive index as a function of photon energy [ Fig. 4(b)]. Here, the refractive index decreases as the photon energy increases in the photon energy intervals 0.76-2.41, 3.66-6.89 and 7.43-8.94 eV. In normal dispersion, the refractive index should increase as the photon energy increases, as observed in the ranges 0-0.76, 2.41-3.66 and 6.89-7.43 eV. It is also interesting to note that when the incident photon energy is greater than 8.52 eV, the value of the refractive index is less than one, which is characteristic of metals. Comparing the refractive index values of the 2D layered Mo 2 CF 2 , the refractive index can be increased by increasing the number of layers. These results suggest that the static dielectric constant and the optical dispersion characteristics of the 2D layered Mo 2 CF 2 can also be manipulated by controlling the number of layers.

Optical properties
The imaginary part of the dielectric function, " 2 (!), is shown in Fig. 5(a). This component is related to the transitions between the valence and conduction bands, and therefore to the electronic structure of Mo 2 CF 2 and the absorption of the incident photons. The optical band gaps of the bulk and 2D layered Mo 2 CF 2 can then be estimated from " 2 (!) and these are 0.220, 0.178 and 0.136 eV for the monolayer, bilayer and trilayer Mo 2 CF 2 , respectively. These optical band gap energies are smaller than the electronic band gap energies obtained from the electronic structures (and summarized in Table 1). The discrepancy comes from the Coulombic interaction between electrons in the conduction band and holes in the valence band, as well as the exclusion of excitonic effects in the approximation (Cadatal-Raduban et al., 2020). Nevertheless, a similar trend to the electronic band gap energy is observed, wherein the optical band gap decreased as the number of layers increased. Above the optical band gap energy, a sharp rise in the intensity of " 2 (!) is observed, with its peak appearing at 1.12 eV for all the materials. The peak corresponds to the electron transitions between the Mo-4d states to the Mo-5d states, as indicated by the density of states of Mo 2 CF 2 (Fig. 3). The absorption coefficient and extinction coefficient of bulk and 2D layered Mo 2 CF 2 is shown in Figs. 5(b) and 5(c), respectively. Regardless of the number of layers, Mo 2 CF 2 is seen to be absorbing over a broad range of photon energies up to the vacuum ultraviolet region (greater than 6 eV photon energy or less than 200 nm wavelength), with a lower photon energy cut-off of 0.429, 0.387 and 0.345 eV for the monolayer, bilayer and trilayer nanosheets, respectively, which is in the mid-infrared wavelength region (wavelengths of about 2890, 3204 and 3594 nm for the monolayer, bilayer and trilayer nanosheets, respectively). Its peak absorption range is in the vacuum ultraviolet region from about 6 to 11 eV (wavelengths of about 207 to 112 nm), with an absorption peak at around 7.9 eV (157 nm). The extinction coefficient measures the loss of photon energy due to absorption and scattering, and therefore mimics the trend of " 2 (!). Like the trend observed for " 2 (!), where the intensity of " 2 (!) increased as the number of layers increased, the value of the absorption and extinction coefficients also increased as a function of the number of layers. This indicates that the absorption of Mo 2 CF 2 can also be manipulated by varying the number of layers. Fig. 6 shows the reflectivity of bulk and 2D layered Mo 2 CF 2 . The reflectivity of the bilayer and trilayer Mo 2 CF 2 are 0.28 and 0.35 at 0 eV, which means that about 28 and 35% of the incident light is reflected. A relatively low reflectivity is observed as the incident photon energy increases. In general, the reflectivity has a decreasing trend at photon energies between about 5 and 12 eV (about 248 and 103 nm). As reflectivity defines the ability of a material to reflect the  incident photons, Mo 2 CF 2 could be suitable as an antireflective coating, especially in the vacuum ultraviolet wavelength region. Furthermore, for this purpose, a smaller number of layers appears to be more advantageous (for example, a monolayer compared to a trilayer) as the general trend is that the reflectivity decreases with a decrease in the number of layers. Fig. 7 shows the optical conductivity of bulk and 2D layered Mo 2 CF 2 . The optical conductivity is derived from " 2 (!) and therefore displays a similar trend compared to the absorption and extinction coefficient spectra [Figs. 5(b)  Reflectivity of bulk and 2D layered Mo 2 CF 2 .

Figure 7
Optical conductivity of bulk and 2D layered Mo 2 CF 2 .  these energy ranges, affirming the metallic behavior of Mo 2 CF 2 at these energy ranges.

Conclusions
Using first principles density functional theory within the generalized gradient approximation (GGA) and the Perdew-Burke-Ernzerhof (PBE) functional, the electronic structure and optical properties of bulk and 2D layered (monolayer, bilayer and trilayer) Mo 2 CF 2 were studied. The band gap energy of the 2D layered Mo 2 CF 2 decreased as the number of layers increased due to interlayer coupling, which resulted in the splitting of the bands. Investigation of the optical properties of Mo 2 CF 2 revealed that it behaves as a metal with an anomalous dispersion in the photon energy intervals of 0.68-2.19, 3.49-6.68 and 7.30-8.31 eV. Mo 2 CF 2 also exhibited a high optical conductivity within these energy intervals. Regardless of the number of layers, Mo 2 CF 2 was seen to be absorbing over a broad range of photon energies up to the vacuum ultraviolet region (greater than 6 eV photon energy or less than 200 nm wavelength), with a lower photon energy cut-off of 0.429 (2890), 0.387 (3204) and 0.345 (3594 nm) for the monolayer, bilayer and trilayer nanosheets, respectively, which is in the mid-infrared wavelength region. Its peak absorption range is in the vacuum ultraviolet region from about 6 to 11 eV (wavelengths of about 207 to 112 nm). A relatively low reflectivity is observed as the incident photon energy increases, particularly at photon energies between about 5 to 12 eV (about 248 to 103 nm). The band gap energy, static dielectric constant, optical dispersion, absorption, extinction coefficient, reflectivity, and conductivity of the 2D layered Mo 2 CF 2 can be manipulated by controlling the number of layers. The unique behavior of its optical properties along with the ability to control its electronic and optical properties indicate the huge potential of 2D layered Mo 2 CF 2 for various applications in the field of electronic devices.